Problem 16 05 Consider the following data relevant to valuing a European style call option on a nondividend paying stock X 40, RFR 10 , T six months (i e , 0 5), and a 0 29 a Compute the Black Scholes option and hedge ratio values for the series of hypothetical current stock price levels shown below You may use Appendix D to answer the question Do not round intermediate calculations Round the Black Scholes option values to the nearest cent and the hedge ratio values to four decimal places Call Hedge Ratio Stock Price b Determine how your answer in Part a would differ under the following separate circumstances (1) the time to expiration decreases, and (2) the volatility of a nondividend paying stock increases A decrease in time to expiration causes a(an) Select in the call value An increase in the volatility causes a(an) Select in the call value c For S 40, calculate the Black Scholes value for a European style put option How much of this value represents time premium Do not round intermediate calculations Round your answers to the nearest cent Put value $ Time premium $ APPENDIX Standard Normal Probabilities 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 09 0 0 0 1 0 2 5359 5753 6141 0 3 6517 6879 0 4 0 5 0 6 0 7 0 8 0 9 5000 5398 5793 6179 6554 6915 7257 7580 7881 8159 8413 8643 8849 9032 9192 7224 7549 7852 8133 7967 8389 1 1 8621 8830 9015 9177 1 2 1 3 1 4 9319 1 5 9332 5040 5438 5832 6217 6591 6950 7291 7611 7910 8186 8438 8665 8860 9049 9207 9345 9463 9564 9649 9719 9778 9826 9864 9896 9920 9940 9955 9966 9975 9982 9987 5080 5120 5478 5517 5871 5910 6255 6293 6628 6664 6985 7019 7324 7357 7642 7673 7939 8212 8238 8461 8485 8686 8708 8888 8907 9066 9082 9222 9236 9357 9370 9474 9484 9573 9582 9656 9664 9726 9732 9783 9788 9830 9834 9868 9871 9898 9901 9922 9925 9943 9956 9957 9967 9968 9976 9977 9982 9983 99879988 5160 5557 5948 6331 6700 7054 7389 7704 7995 8264 8508 8729 8925 9099 9251 9382 9495 9591 9671 9738 9793 9838 9875 9904 9927 9945 9959 9969 9977 9984 9988 5199 5596 5987 6368 6736 7088 7422 7734 8023 8289 8531 8749 8943 9115 9265 9394 9505 9599 9678 9744 9798 9842 9878 9906 9929 9946 9960 9970 9978 9984 9989 5239 5279 5636 5675 6026 6064 6406 6443 6772 6808 7123 7157 7454 7486 7764 7794 8051 8078 8315 8340 8554 8577 8770 8790 8962 8980 9131 9147 9279 9292 9406 9418 9515 9525 9608 9616 9686 9693 9750 9756 9803 9808 9846 9850 9881 9884 9909 9911 9931 9932 9948 9949 9961 9962 9971 9972 9979 9979 9985 9985 99899989 5219 5714 6103 6480 6844 7190 7517 7823 8106 8365 8599 8810 8997 9162 9306 9429 9535 9625 9699 9761 9812 9854 9887 9913 ,9934 ,9951 9963 9973 9980 9986 9990 1 6 1 7 1 8 1 9 2 0 2 1 2 2 9441 9545 9633 9706 9767 9817 9857 9890 9916 9936 9952 9964 9974 9981 9986 9990 9452 9554 9641 9713 9772 9821 9861 9893 9918 9938 9953 9965 9974 9981 9987 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0 9941 Problem 16 05 Consider the following data relevant to valuing a European style call option on a nondividend paying stock X 40, RFR 10 , T six months (i e , 0 5), and a 0 29 a Compute the Black Scholes option and hedge ratio values for the series of hypothetical current stock price levels shown below You may use Appendix D to answer the question Do not round intermediate calculations Round the Black Scholes option values to the nearest cent and the hedge ratio values to four decimal places Call Hedge Ratio Stock Price b Determine how your answer in Part a would differ under the following separate circumstances (1) the time to expiration decreases, and (2) the volatility of a nondividend paying stock increases A decrease in time to expiration causes a(an) Select in the call value An increase in the volatility causes a(an) Select in the call value c For S 40, calculate the Black Scholes value for a European style put option How much of this value represents time premium Do not round intermediate calculations Round your answers to the nearest cent Put value $ Time premium $ APPENDIX Standard Normal Probabilities 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 09 0 0 0 1 0 2 5359 5753 6141 0 3 6517 6879 0 4 0 5 0 6 0 7 0 8 0 9 5000 5398 5793 6179 6554 6915 7257 7580 7881 8159 8413 8643 8849 9032 9192 7224 7549 7852 8133 7967 8389 1 1 8621 8830 9015 9177 1 2 1 3 1 4 9319 1 5 9332 5040 5438 5832 6217 6591 6950 7291 7611 7910 8186 8438 8665 8860 9049 9207 9345 9463 9564 9649 9719 9778 9826 9864 9896 9920 9940 9955 9966 9975 9982 9987 5080 5120 5478 5517 5871 5910 6255 6293 6628 6664 6985 7019 7324 7357 7642 7673 7939 8212 8238 8461 8485 8686 8708 8888 8907 9066 9082 9222 9236 9357 9370 9474 9484 9573 9582 9656 9664 9726 9732 9783 9788 9830 9834 9868 9871 9898 9901 9922 9925 9943 9956 9957 9967 9968 9976 9977 9982 9983 99879988 5160 5557 5948 6331 6700 7054 7389 7704 7995 8264 8508 8729 8925 9099 9251 9382 9495 9591 9671 9738 9793 9838 9875 9904 9927 9945 9959 9969 9977 9984 9988 5199 5596 5987 6368 6736 7088 7422 7734 8023 8289 8531 8749 8943 9115 9265 9394 9505 9599 9678 9744 9798 9842 9878 9906 9929 9946 9960 9970 9978 9984 9989 5239 5279 5636 5675 6026 6064 6406 6443 6772 6808 7123 7157 7454 7486 7764 7794 8051 8078 8315 8340 8554 8577 8770 8790 8962 8980 9131 9147 9279 9292 9406 9418 9515 9525 9608 9616 9686 9693 9750 9756 9803 9808 9846 9850 9881 9884 9909 9911 9931 9932 9948 9949 9961 9962 9971 9972 9979 9979 9985 9985 99899989 5219 5714 6103 6480 6844 7190 7517 7823 8106 8365 8599 8810 8997 9162 9306 9429 9535 9625 9699 9761 9812 9854 9887 9913 ,9934 ,9951 9963 9973 9980 9986 9990 1 6 1 7 1 8 1 9 2 0 2 1 2 2 9441 9545 9633 9706 9767 9817 9857 9890 9916 9936 9952 9964 9974 9981 9986 9990 9452 9554 9641 9713 9772 9821 9861 9893 9918 9938 9953 9965 9974 9981 9987 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0 9941

Question

Problem 16 05 Consider the following data relevant to valuing a European style call option on a nondividend paying stock  X   40, RFR   10 , T   six months (i e , 0 5), and a   0 29  a  Compute the Black Scholes option and hedge ratio values for the series of hypothetical current stock price levels shown below  You may use Appendix D to answer the question  Do not round intermediate calculations  Round the Black Scholes option values to the nearest cent and the hedge ratio values to four decimal places  Call Hedge Ratio Stock Price b  Determine how your answer in Part a would differ under the following separate circumstances  (1) the time to expiration decreases, and (2) the volatility of a nondividend paying stock increases  A decrease in time to expiration causes a(an)  Select  in the call value  An increase in the volatility causes a(an)  Select  in the call value  c  For S   40, calculate the Black Scholes value for a European style put option  How much of this value represents time premium  Do not round intermediate calculations  Round your answers to the nearest cent  Put value  $ Time premium  $ APPENDIX Standard Normal Probabilities 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 09 0 0 0 1 0 2  5359  5753  6141 0 3  6517  6879 0 4 0 5 0 6 0 7 0 8 0 9  5000  5398  5793  6179  6554  6915  7257  7580  7881  8159  8413  8643  8849  9032  9192  7224  7549  7852  8133  7967  8389 1 1  8621  8830  9015  9177 1 2 1 3 1 4  9319 1 5  9332 5040  5438  5832  6217  6591  6950  7291  7611  7910  8186  8438  8665  8860  9049 9207 9345 9463 9564 9649 9719  9778  9826 9864  9896  9920  9940 9955 9966  9975  9982  9987 5080  5120  5478 5517  5871  5910  6255  6293  6628  6664  6985  7019  7324  7357  7642  7673  7939  8212  8238  8461  8485  8686  8708  8888  8907  9066  9082  9222  9236 9357 9370 9474 9484 9573  9582  9656 9664 9726  9732 9783 9788  9830 9834  9868 9871 9898 9901  9922 9925 9943  9956  9957 9967 9968 9976  9977 9982 9983 99879988 5160 5557 5948  6331 6700 7054  7389  7704  7995  8264  8508  8729  8925 9099  9251  9382  9495  9591  9671  9738 9793 9838  9875  9904 9927  9945  9959  9969  9977  9984  9988  5199  5596 5987  6368  6736  7088  7422  7734  8023  8289  8531  8749  8943  9115 9265  9394  9505  9599  9678  9744  9798 9842  9878  9906  9929  9946  9960  9970  9978 9984 9989 5239  5279  5636  5675  6026  6064  6406 6443  6772  6808  7123  7157  7454  7486  7764  7794  8051  8078  8315  8340  8554  8577  8770  8790  8962  8980  9131 9147 9279 9292 9406 9418 9515 9525  9608 9616  9686 9693  9750 9756 9803 9808  9846  9850  9881  9884  9909  9911  9931  9932  9948  9949  9961 9962  9971  9972  9979  9979 9985  9985 99899989  5219  5714  6103  6480  6844  7190  7517 7823  8106  8365  8599  8810  8997 9162 9306 9429  9535 9625  9699  9761 9812 9854 9887 9913 ,9934 ,9951  9963  9973  9980  9986  9990 1 6 1 7 1 8 1 9 2 0 2 1 2 2 9441  9545  9633  9706  9767  9817 9857  9890  9916  9936  9952  9964 9974 9981 9986 9990  9452 9554  9641  9713  9772  9821  9861  9893  9918  9938  9953  9965  9974  9981  9987 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0  9941 Problem 16 05 Consider the following data relevant to valuing a European style call option on a nondividend paying stock  X   40, RFR   10 , T   six months (i e , 0 5), and a   0 29  a  Compute the Black Scholes option and hedge ratio values for the series of hypothetical current stock price levels shown below  You may use Appendix D to answer the question  Do not round intermediate calculations  Round the Black Scholes option values to the nearest cent and the hedge ratio values to four decimal places  Call Hedge Ratio Stock Price b  Determine how your answer in Part a would differ under the following separate circumstances  (1) the time to expiration decreases, and (2) the volatility of a nondividend paying stock increases  A decrease in time to expiration causes a(an)  Select  in the call value  An increase in the volatility causes a(an)  Select  in the call value  c  For S   40, calculate the Black Scholes value for a European style put option  How much of this value represents time premium  Do not round intermediate calculations  Round your answers to the nearest cent  Put value  $ Time premium  $ APPENDIX Standard Normal Probabilities 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 09 0 0 0 1 0 2  5359  5753  6141 0 3  6517  6879 0 4 0 5 0 6 0 7 0 8 0 9  5000  5398  5793  6179  6554  6915  7257  7580  7881  8159  8413  8643  8849  9032  9192  7224  7549  7852  8133  7967  8389 1 1  8621  8830  9015  9177 1 2 1 3 1 4  9319 1 5  9332 5040  5438  5832  6217  6591  6950  7291  7611  7910  8186  8438  8665  8860  9049 9207 9345 9463 9564 9649 9719  9778  9826 9864  9896  9920  9940 9955 9966  9975  9982  9987 5080  5120  5478 5517  5871  5910  6255  6293  6628  6664  6985  7019  7324  7357  7642  7673  7939  8212  8238  8461  8485  8686  8708  8888  8907  9066  9082  9222  9236 9357 9370 9474 9484 9573  9582  9656 9664 9726  9732 9783 9788  9830 9834  9868 9871 9898 9901  9922 9925 9943  9956  9957 9967 9968 9976  9977 9982 9983 99879988 5160 5557 5948  6331 6700 7054  7389  7704  7995  8264  8508  8729  8925 9099  9251  9382  9495  9591  9671  9738 9793 9838  9875  9904 9927  9945  9959  9969  9977  9984  9988  5199  5596 5987  6368  6736  7088  7422  7734  8023  8289  8531  8749  8943  9115 9265  9394  9505  9599  9678  9744  9798 9842  9878  9906  9929  9946  9960  9970  9978 9984 9989 5239  5279  5636  5675  6026  6064  6406 6443  6772  6808  7123  7157  7454  7486  7764  7794  8051  8078  8315  8340  8554  8577  8770  8790  8962  8980  9131 9147 9279 9292 9406 9418 9515 9525  9608 9616  9686 9693  9750 9756 9803 9808  9846  9850  9881  9884  9909  9911  9931  9932  9948  9949  9961 9962  9971  9972  9979  9979 9985  9985 99899989  5219  5714  6103  6480  6844  7190  7517 7823  8106  8365  8599  8810  8997 9162 9306 9429  9535 9625  9699  9761 9812 9854 9887 9913 ,9934 ,9951  9963  9973  9980  9986  9990 1 6 1 7 1 8 1 9 2 0 2 1 2 2 9441  9545  9633  9706  9767  9817 9857  9890  9916  9936  9952  9964 9974 9981 9986 9990  9452 9554  9641  9713  9772  9821  9861  9893  9918  9938  9953  9965  9974  9981  9987 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0  9941

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Problem 16-05 Consider the following data relevant to valuing a European-style call option on a nondividend-paying stock: X = 40, RFR = 10%, T =

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